This 86th episode of Learning Machines 101 discusses the problem of assigning probabilities to a possibly infinite set of outcomes in a space-time continuum which characterizes our physical world. Such a set is called an “environmental event”. The machine learning algorithm uses information about the frequency of environmental events to support learning. If we want to study statistical machine learning, then we must be able to discuss how to represent and compute the probability of an environmental event. It is essential that we have methods for communicating probability concepts to other researchers, methods for calculating probabilities, and methods for calculating the expectation of specific environmental events. This episode discusses the challenges of assigning probabilities to events when we allow for the case of events comprised of an infinite number of outcomes. Along the way we introduce essential concepts for representing and computing probabilities using measure theory mathematical tools such as sigma fields, and the Radon-Nikodym probability density function. Near the end we also briefly discuss the intriguing Banach-Tarski paradox and how it motivates the development of some of these special mathematical tools. Check out: www.learningmachines101.com and www.statisticalmachinelearning.com for more information!!!
LM101-026: How to Learn Statistical Regularities (Rerun)
LM101-025: How to Build a Lunar Lander Autopilot Learning Machine
LM101-024: How to Use Genetic Algorithms to Breed Learning Machines
LM101-023: How to Build a Deep Learning Machine
LM101-022: How to Learn to Solve Large Constraint Satisfaction Problems
LM101-021: How to Solve Large Complex Constraint Satisfaction Problems (Monte Carlo Markov Chain)
LM101-020: How to Use Nonlinear Machine Learning Software to Make Predictions
LM101-019 (Rerun): How to Enhance Intelligence with a Robotic Body (Embodied Cognition)
LM101-018: Can Computers Think? A Mathematician's Response (Rerun)
LM101-017: How to Decide if a Machine is Artificially Intelligent (Rerun)
LM101-016: How to Analyze and Design Learning Rules using Gradient Descent Methods
LM101-015: How to Build a Machine that Can Learn Anything (The Perceptron)
LM101-014: How to Build a Machine that Can Do Anything (Function Approximation)
LM101-013: How to Use Linear Machine Learning Software to Make Predictions (Linear Regression Software)
LM101-012: How to Evaluate the Ability to Generalize from Experience (Cross-Validation Methods)
LM101-008: How to Represent Beliefs Using Probability Theory
LM101-011: How to Learn About Rare and Unseen Events (Smoothing Probabilistic Laws)
LM101-010: How to Learn Statistical Regularities (MAP and maximum likelihood estimation)
LM101-009: How to Enhance Intelligence with a Robotic Body (Embodied Cognition)
LM101-007: How to Reason About Uncertain Events using Fuzzy Set Theory and Fuzzy Measure Theory
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